Logical meaning in space: Iconic biases on quantification in sign languages

Typologically, the world's languages vary in how they express universal quantification and negative quantification. In patterns of concord, a single distributive or negative meaning is expressed redundantly on multiple morphological items. Sign languages, too, show semantic variation, but, surprisingly, this variation populates a specific corner of the full typological landscape. When we focus on manual signs, sign languages systematically have distributive concord but tend to not have negative concord in its canonical form. Here, I explain these typological facts as the reflection of an abstract, iconic bias. Recent work on distributive concord and negative concord has proposed that the phenomena can be explained in relation to the discourse referents they make available. The use of space in sign language also invites iconic inferences about the referents introduced in discourse. I show that these iconic inferences coincide with the meaning of distributive concord but contradict the meaning of negative concord. The sign language typology is thus explained based on what is easy and hard to represent in space.